In this paper, we prove that a compact quasi-Einstein manifold $(M^n,\,g,\,u)$ of dimension $n\geq 4$ with boundary $\partial M,$ nonnegative sectional curvature and zero radial Weyl tensor is either isometric, up to scaling, the standard hemisphere $\Bbb {S}^n_+,$ or $g=dt^{2}+\psi ^{2}(t)g_{L}$ $u=u(t),$ where $g_{L}$ Einstein Ricci curvature. A similar classification result obtained by assum...

In this paper, we defined two new games - the mildly Menger game and compact-clopen game. a zero-dimensional space, is equivalent to compact-open An example given for space on which undetermined. Also introduced namely K-quasi-component-clopen proved that Then if topological union of countably many quasi-components compact sets, then TWO has winning strategy in